i've had this quest since, like, i began playing this game:

** Talk to the arena Bookie, then join a random arena battle and win. Return to the Gladiator after you've won a match.

i go to the arena and click random battle, if not multiple times a day, at least once a day, and still have never been able to find someone to battle with.

should i bother to keep trying to do this or is it something i just can't finish?

Rima there are 2 ways to overcome that.
1. coordinate through bw2 chat or other djarts chats with someone to go join you.
2. have someone you know personally, like a second version of you if you have multiple accounts, go there and click on random battle (i,e, don't click on the friend itself).
doing either can help with the daily quest, or to help you build up arena tokens, or o work through some of the arena achievements. you don't have to win in order to get some tokens, but you do get more when you do win.

I have done #2 once or twice when at a library computer that was powerful enough to have 2 copies of bw1 open in 2 different browsers at the same time.

I don't know what the daily dau or monthly mau numbers for bw1 are, but bw2 only has 3,500 and 9,000 so I imagine a whole lot fewer in bw1, and nobody else ever in the arena when you need them cause like you they never see anyone else.